The use of nerve stimulation for treating and controlling a variety of medical, psychiatric, and neurological disorders has seen significant growth over the last several decades. In particular, stimulation of the vagus nerve (the tenth cranial nerve, and part of the parasympathetic nervous system) has been the subject of considerable research. The vagus nerve is composed of somatic and visceral afferents (inward conducting nerve fibers, which convey impulses toward the brain) and efferents (outward conducting nerve fibers, which convey impulses to an effector to regulate activity such as muscle contraction or glandular secretion).
The rate of the heart is restrained in part by parasympathetic stimulation from the right and left vagus nerves. Low vagal nerve activity is considered to be related to various arrhythmias, including tachycardia, ventricular accelerated rhythm, and rapid atrial fibrillation. By artificially stimulating the vagus nerves, it is possible to slow the heart, allowing the heart to more completely relax and the ventricles to experience increased filling. With larger diastolic volumes, the heart may beat more efficiently because it may expend less energy to overcome the myocardial viscosity and elastic forces of the heart with each beat.
Stimulation of the vagus nerve has been proposed as a method for treating various heart conditions, including heart failure and atrial fibrillation. Heart failure is a cardiac condition characterized by a deficiency in the ability of the heart to pump blood throughout the body and/or to prevent blood from backing up in the lungs. Customary treatment of heart failure includes medication and lifestyle changes. It is often desirable to lower the heart rates of patients suffering from faster than normal heart rates. The effectiveness of beta blockers in treating heart disease is attributed in part to their heart-rate-lowering effect.
Bilgutay et al., in “Vagal tuning: a new concept in the treatment of supraventricular arrhythmias, angina pectoris, and heart failure,” J. Thoracic Cardiovas. Surg. 56(1):71-82, July, 1968, which is incorporated herein by reference, studied the use of a permanently-implanted device with electrodes to stimulate the right vagus nerve for treatment of supraventricular arrhythmias, angina pectoris, and heart failure. Experiments were conducted to determine amplitudes, frequencies, wave shapes and pulse lengths of the stimulating current to achieve slowing of the heart rate. The authors additionally studied an external device, triggered by the R-wave of the electrocardiogram (ECG) of the subject to provide stimulation only upon an achievement of a certain heart rate. They found that when a pulsatile current with a frequency of ten pulses per second and 0.2 milliseconds pulse duration was applied to the vagus nerve, the heart rate could be decreased to half the resting rate while still preserving sinus rhythm. Low amplitude vagal stimulation was employed to control induced tachycardias and ectopic beats. The authors further studied the use of the implanted device in conjunction with the administration of Isuprel, a sympathomimetic drug. They found that Isuprel retained its inotropic effect of increasing contractility, while its chronotropic effect was controlled by the vagal stimulation: “An increased end diastolic volume brought about by slowing of the heart rate by vagal tuning, coupled with increased contractility of the heart induced by the inotropic effect of Isuprel, appeared to increase the efficiency of cardiac performance” (p. 79).
U.S. Pat. No. 6,473,644 to Terry, Jr. et al., which is incorporated herein by reference, describes a method for treating patients suffering from heart failure to increase cardiac output, by stimulating or modulating the vagus nerve with a sequence of substantially equally-spaced pulses by an implanted neurostimulator. The frequency of the stimulating pulses is adjusted until the patient's heart rate reaches a target rate within a relatively stable target rate range below the low end of the patient's customary resting heart rate.
U.S. Patent Application Publication 2003/0040774 to Terry et al., which is incorporated herein by reference, describes a device for treating patients suffering from congestive heart failure. The device includes an implantable neurostimulator for stimulating the patient's vagus nerve at or above the cardiac branch with an electrical pulse waveform at a stimulating rate sufficient to maintain the patient's heart beat at a rate well below the patient's normal resting heart rate, thereby allowing rest and recovery of the heart muscle, to increase in coronary blood flow, and/or growth of coronary capillaries. A metabolic need sensor detects the patient's current physical state and concomitantly supplies a control signal to the neurostimulator to vary the stimulating rate. If the detection indicates a state of rest, the neurostimulator rate reduces the patient's heart rate below the patient's normal resting rate. If the detection indicates physical exertion, the neurostimulator rate increases the patient's heart rate above the normal resting rate.
US Patent Publication 2003/0045909 to Gross et al., which is assigned to the assignee of the present patent application and is incorporated herein by reference, describes apparatus for treating a heart condition of a subject, including an electrode device, which is adapted to be coupled to a vagus nerve of the subject. A control unit is adapted to drive the electrode device to apply to the vagus nerve a stimulating current, which is capable of inducing action potentials in a therapeutic direction in a first set and a second set of nerve fibers of the vagus nerve. The control unit is also adapted to drive the electrode device to apply to the vagus nerve an inhibiting current, which is capable of inhibiting the induced action potentials traveling in the therapeutic direction in the second set of nerve fibers, the nerve fibers in the second set having generally larger diameters than the nerve fibers in the first set.
The effect of vagal stimulation on heart rate and other aspects of heart function, including the relationship between the timing of vagal stimulation within the cardiac cycle and the induced effect on heart rate, has been studied in animals. For example, Zhang Y et al., in “Optimal ventricular rate slowing during atrial fibrillation by feedback AV nodal-selective vagal stimulation,” Am J Physiol Heart Circ Physiol 282:H1102-H1110 (2002), describe the application of selective vagal stimulation by varying the nerve stimulation intensity, in order to achieve graded slowing of heart rate. This article is incorporated herein by reference.
The following articles and book, which are incorporated herein by reference, may be of interest:
Levy M N et al., in “Parasympathetic Control of the Heart,” Nervous Control of Vascular Function, Randall W C ed., Oxford University Press (1984)
Levy M N et al. ed., Vagal Control of the Heart: Experimental Basis and Clinical Implications (The Bakken Research Center Series Volume 7), Futura Publishing Company, Inc., Armonk, N.Y. (1993)
Randall W C ed., Neural Regulation of the Heart, Oxford University Press (1977), particularly pages 100-106.
Armour J A et al. eds., Neurocardiology, Oxford University Press (1994)
Perez M G et al., “Effect of stimulating non-myelinated vagal axon on atrio-ventricular conduction and left ventricular function in anaesthetized rabbits,” Auton Neurosco 86 (2001)
Jones, J F X et al., “Heart rate responses to selective stimulation of cardiac vagal C fibres in anaesthetized cats, rats and rabbits,” J Physiol 489 (Pt 1):203-14 (1995)
Wallick D W et al., “Effects of ouabain and vagal stimulation on heart rate in the dog,” Cardiovasc. Res., 18(2):75-9 (1984)
Martin P J et al., “Phasic effects of repetitive vagal stimulation on atrial contraction,” Circ. Res. 52(6):657-63 (1983)
Wallick D W et al., “Effects of repetitive bursts of vagal activity on atrioventricular junctional rate in dogs,” Am J Physiol 237(3):H275-81 (1979)
Fuster V and Ryden L E et al., “ACC/AHA/ESC Practice Guidelines—Executive Summary,” J Am Coll Cardiol 38(4):1231-65 (2001)
Fuster V and Ryden L E et al., “ACC/AHA/ESC Practice Guidelines—Full Text,” J Am Coll Cardiol 38(4):1266i-12661xx (2001)
Morady F et al., “Effects of resting vagal tone on accessory atrioventricular connections,” Circulation 81(1):86-90 (1990)
Waninger M S et al., “Electrophysiological control of ventricular rate during atrial fibrillation,” PACE 23:1239-1244 (2000)
Wijffels M C et al., “Electrical remodeling due to atrial fibrillation in chronically instrumented conscious goats: roles of neurohumoral changes, ischemia, atrial stretch, and high rate of electrical activation,” Circulation 96(10):3710-20 (1997)
Wijffels M C et al., “Atrial fibrillation begets atrial fibrillation,” Circulation 92:1954-1968 (1995)
Goldberger A L et al., “Vagally-mediated atrial fibrillation in dogs: conversion with bretylium tosylate,” Int J Cardiol 13(1):47-55 (1986)
Takei M et al., “Vagal stimulation prior to atrial rapid pacing protects the atrium from electrical remodeling in anesthetized dogs,” Jpn Circ J 65(12):1077-81 (2001)
Friedrichs G S, “Experimental models of atrial fibrillation/flutter,” J Pharmacological and Toxicological Methods 43:117-123 (2000)
Hayashi H et al., “Different effects of class Ic and III antiarrhythmic drugs on vagotonic atrial fibrillation in the canine heart,” Journal of Cardiovascular Pharmacology 31:101-107 (1998)
Morillo C A et al., “Chronic rapid atrial pacing. Structural, functional, and electrophysiological characteristics of a new model of sustained atrial fibrillation,” Circulation 91:1588-1595 (1995)
Lew S J et al., “Stroke prevention in elderly patients with atrial fibrillation,” Singapore Med J 43(4):198-201 (2002)
Higgins C B, “Parasympathetic control of the heart,” Pharmacol. Rev. 25:120-155 (1973)
Hunt R, “Experiments on the relations of the inhibitory to the accelerator nerves of the heart,” J. Exptl. Med. 2:151-179 (1897)
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Garrigue S et al., “Post-ganglionic vagal stimulation of the atrioventricular node reduces ventricular rate during atrial fibrillation,” PACE 21(4), 878 (Part II) (1998)
Kwan H et al., “Cardiovascular adverse drug reactions during initiation of antiarrhythmic therapy for atrial fibrillation, ” Can J Hosp Pharm 54:10-14 (2001)
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Heart rate variability is considered an important determinant of cardiac function. Heart rate normally fluctuates within a normal range in order to accommodate constantly changing physiological needs. For example, heart rate increases during waking hours, exertion, and inspiration, and decreases during sleeping, relaxation, and expiration. Two representations of heart rate variability are commonly used: (a) the standard deviation of beat-to-beat RR interval differences within a certain time window (i.e., variability in the time domain), and (b) the magnitude of variability as a function of frequency (i.e., variability in the frequency domain).
Short-term (beat-to-beat) variability in heart rate represents fast, high-frequency (HF) changes in heart rate. For example, the changes in heart rate associated with breathing are characterized by a frequency of between about 0.15 and about 0.4 Hz (corresponding to a time constant between about 2.5 and 7 seconds). Low-frequency (LF) changes in heart rate (for example, blood pressure variations) are characterized by a frequency of between about 0.04 and about 0.15 Hz (corresponding to a time constant between about 7 and 25 seconds). Very-low-frequency (VLF) changes in heart rate are characterized by a frequency of between about 0.003 and about 0.04 Hz (0.5 to 5 minutes). Ultra-low-frequency (ULF) changes in heart rate are characterized by a frequency of between about 0.0001 and about 0.003 Hz (5 minutes to 2.75 hours). A commonly used indicator of heart rate variability is the ratio of HF power to LF power.
High heart rate variability (especially in the high frequency range, as described hereinabove) is generally correlated with a good prognosis in conditions such as ischemic heart disease and heart failure. In other conditions, such as atrial fibrillation, increased heart rate variability in an even higher frequency range can cause a reduction in cardiac efficiency by producing beats that arrive too quickly (when the ventricle is not optimally filled) and beats that arrive too late (when the ventricle is fully filled and the pressure is too high).
Kamath et al., in “Effect of vagal nerve electrostimulation on the power spectrum of heart rate variability in man,” Pacing Clin Electrophysiol 15:235-43 (1992), describe an increase in the ratio of low frequency to high frequency components of the peak power spectrum of heart rate variability during a period without vagal stimulation, compared to periods with vagal stimulation. Iwao et al., in “Effect of constant and intermittent vagal stimulation on the heart rate and heart rate variability in rabbits,” Jpn J Physiol 50:33-9 (2000), describe no change in heart rate variability caused by respiration in all modes of stimulation with respect to baseline data. Each of these articles is incorporated herein by reference.
The following articles, which are incorporated herein by reference, may be of interest:
Kleiger RE et al., “Decreased heart rate variability and its association with increased mortality after myocardial infarction,” Am J Cardiol 59: 256-262 (1987)
Akselrod S et al., “Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control,” Science 213: 220-222 (1981)
A number of patents describe techniques for treating arrhythmias and/or ischemia by, at least in part, stimulating the vagus nerve. Arrhythmias in which the heart rate is too fast include fibrillation, flutter and tachycardia. Arrhythmia in which the heart rate is too slow is known as bradyarrhythmia. U.S. Pat. No. 5,700,282 to Zabara, which is incorporated herein by reference, describes techniques for stabilizing the heart rhythm of a patient by detecting arrhythmias and then electronically stimulating the vagus and cardiac sympathetic nerves of the patient. The stimulation of vagus efferents directly causes the heart rate to slow down, while the stimulation of cardiac sympathetic nerve efferents causes the heart rate to quicken.
U.S. Pat. No. 5,330,507 to Schwartz, which is incorporated herein by reference, describes a cardiac pacemaker for preventing or interrupting tachyarrhythmias and for applying pacing therapies to maintain the heart rhythm of a patient within acceptable limits. The device automatically stimulates the right or left vagus nerves as well as the cardiac tissue in a concerted fashion dependent upon need. Continuous and/or phasic electrical pulses are applied. Phasic pulses are applied in a specific relationship with the R-wave of the ECG of the patient.
European Patent Application EP 0 688 577 to Holmstrom et al., which is incorporated herein by reference, describes a device to treat atrial tachyarrhythmia by detecting arrhythmia and stimulating a parasympathetic nerve that innervates the heart, such as the vagus nerve.
U.S. Pat. Nos. 5,690,681 and 5,916,239 to Geddes et al., which are incorporated herein by reference, describe closed-loop, variable-frequency, vagal-stimulation apparatus for control of ventricular rate during atrial fibrillation. The apparatus stimulates the left vagus nerve, and automatically and continuously adjusts the vagal stimulation frequency as a function of the difference between actual and desired ventricular excitation rates. In an alternative embodiment, the apparatus automatically adjusts the vagal stimulation frequency as a function of the difference between ventricular excitation rate and arterial pulse rate in order to eliminate or minimize pulse deficit.
U.S. Pat. No. 5,203,326 to Collins, which is incorporated herein by reference, describes a pacemaker which detects a cardiac abnormality and responds with electrical stimulation of the heart combined with vagus nerve stimulation. The vagal stimulation frequency is progressively increased in one-minute intervals, and, for the pulse delivery rate selected, the heart rate is described as being slowed to a desired, stable level by increasing the pulse current.
U.S. Pat. No. 6,511,500 to Rahme, which is incorporated herein by reference, describes various aspects of the effects of autonomic nervous system tone on atrial arrhythmias, and its interaction with class III antiarrhythmic drug effects. The significance of sympathetic and parasympathetic activation are described as being evaluated by determining the effects of autonomic nervous system using vagal and stellar ganglions stimulation, and by using autonomic nervous system neurotransmitters infusion (norepinephrine, acetylcholine).
U.S. Pat. No. 5,199,428 to Obel et al., which is incorporated herein by reference, describes a cardiac pacemaker for detecting and treating myocardial ischemia. The device automatically stimulates the vagal nervous system as well as the cardiac tissue in a concerted fashion in order to decrease cardiac workload and thereby protect the myocardium.
U.S. Pat. No. 5,334,221 to Bardy and U.S. Pat. No. 5,356,425 to Bardy et al., which are incorporated herein by reference, describe a stimulator for applying stimulus pulses to the AV nodal fat pad in response to the heart rate exceeding a predetermined rate, in order to reduce the ventricular rate. The device also includes a cardiac pacemaker which serves to pace the ventricle in the event that the ventricular rate is lowered below a pacing rate, and provides for feedback control of the stimulus parameters applied to the AV nodal fat pad, as a function of the determined effect of the stimulus pulses on the heart rate.
U.S. Pat. No. 5,522,854 to Ideker et al., which is incorporated herein by reference, describes techniques for preventing arrhythmia by detecting a high risk of arrhythmia and then stimulating afferent nerves to prevent the arrhythmia.
U.S. Pat. No. 6,434,424 to Igel et al., which is incorporated herein by reference, describes a pacing system with a mode switching feature and ventricular rate regularization function adapted to stabilize or regularize ventricular heart rate during chronic or paroxysmal atrial tachyarrhythmia.
US Patent Application Publication 2002/0120304 to Mest, which is incorporated herein by reference, describes a method for regulating the heart rate of a patient by inserting into a blood vessel of the patient a catheter having an electrode at its distal end, and directing the catheter to an intravascular location so that the electrode is adjacent to a selected cardiac sympathetic or parasympathetic nerve.
U.S. Pat. Nos. 6,006,134 and 6,266,564 to Hill et al., which are incorporated herein by reference, describe an electro-stimulation device including a pair of electrodes for connection to at least one location in the body that affects or regulates the heartbeat.
PCT Publication WO 02/085448 to Foreman et al., which is incorporated herein by reference, describes a method for protecting cardiac function and reducing the impact of ischemia on the heart, by electrically stimulating a neural structure capable of carrying the predetermined electrical signal from the neural structure to the “intrinsic cardiac nervous system,” which is defined and described therein.
U.S. Pat. No. 5,243,980 to Mehra, which is incorporated herein by reference, describes techniques for discrimination between ventricular and supraventricular tachycardia. In response to the detection of the occurrence of a tachycardia, stimulus pulses are delivered to one or both of the SA and AV nodal fat pads. The response of the heart rhythm to these stimulus pulses is monitored. Depending upon the change or lack of change in the heart rhythm, a diagnosis is made as to the origin of the tachycardia.
U.S. Pat. No. 5,658,318 to Stroetmann et al., which is incorporated herein by reference, describes a device for detecting a state of imminent cardiac arrhythmia in response to activity in nerve signals conveying information from the autonomic nerve system to the heart. The device comprises a sensor adapted to be placed in an extracardiac position and to detect activity in at least one of the sympathetic and vagus nerves.
U.S. Pat. No. 6,292,695 to Webster, Jr. et al., which is incorporated herein by reference, describes a method for controlling cardiac fibrillation, tachycardia, or cardiac arrhythmia by the use of a catheter comprising a stimulating electrode, which is placed at an intravascular location. The electrode is connected to a stimulating means, and stimulation is applied across the wall of the vessel, transvascularly, to a sympathetic or parasympathetic nerve that innervates the heart at a strength sufficient to depolarize the nerve and effect the control of the heart.
U.S. Pat. No. 6,134,470 to Hartlaub, which is incorporated herein by reference, describes an implantable anti-arrhythmia system which includes a spinal cord stimulator coupled to an implantable heart rhythm monitor. The monitor is adapted to detect the occurrence of tachyarrhythmias or of precursors thereto and, in response, trigger the operation of the spinal cord stimulator in order to prevent occurrences of tachyarrhythmias and/or as a stand-alone therapy for termination of tachyarrhythmias and/or to reduce the level of aggressiveness required of an additional therapy such as antitachycardia pacing, cardioversion or defibrillation.
A number of patents and articles describe other methods and devices for stimulating nerves to achieve a desired effect. Often these techniques include a design for an electrode or electrode cuff.
US Patent Publication 2003/0050677 to Gross et al., which is assigned to the assignee of the present patent application and is incorporated herein by reference, describes apparatus for applying current to a nerve. A cathode is adapted to be placed in a vicinity of a cathodic longitudinal site of the nerve and to apply a cathodic current to the nerve. A primary inhibiting anode is adapted to be placed in a vicinity of a primary anodal longitudinal site of the nerve and to apply a primary anodal current to the nerve. A secondary inhibiting anode is adapted to be placed in a vicinity of a secondary anodal longitudinal site of the nerve and to apply a secondary anodal current to the nerve, the secondary anodal longitudinal site being closer to the primary anodal longitudinal site than to the cathodic longitudinal site.
U.S. Pat. No. 4,608,985 to Crish et al. and U.S. Pat. No. 4,649,936 to Ungar et al., which are incorporated herein by reference, describe electrode cuffs for selectively blocking orthodromic action potentials passing along a nerve trunk, in a manner intended to avoid causing nerve damage.
PCT Patent Publication WO 01/10375 to Felsen et al., which is incorporated herein by reference, describes apparatus for modifying the electrical behavior of nervous tissue. Electrical energy is applied with an electrode to a nerve in order to selectively inhibit propagation of an action potential.
U.S. Pat. No. 5,755,750 to Petruska et al., which is incorporated herein by reference, describes techniques for selectively blocking different size fibers of a nerve by applying direct electric current between an anode and a cathode that is larger than the anode. The current applied to the electrodes blocks nerve transmission, but, as described, does not activate the nerve fibers in either direction.
The following articles, which are incorporated herein by reference, may be of interest:
Ungar I J et al., “Generation of unidirectionally propagating action potentials using a monopolar electrode cuff,” Annals of Biomedical Engineering, 14:437-450 (1986)
Sweeney J D et al., “An asymmetric two electrode cuff for generation of unidirectionally propagated action potentials,” IEEE Transactions on Biomedical Engineering, vol. BME-33(6) (1986)
Sweeney J D et al., “A nerve cuff technique for selective excitation of peripheral nerve trunk regions,” IEEE Transactions on Biomedical Engineering, 37(7) (1990)
Naples G G et al., “A spiral nerve cuff electrode for peripheral nerve stimulation,” by IEEE Transactions on Biomedical Engineering, 35(11) (1988)
van den Honert C et al., “Generation of unidirectionally propagated action potentials in a peripheral nerve by brief stimuli,” Science, 206:1311-1312 (1979)
van den Honert C et al., “A technique for collision block of peripheral nerve: Single stimulus analysis,” MP-11, IEEE Trans. Biomed. Eng. 28:373-378 (1981)
van den Honert C et al., “A technique for collision block of peripheral nerve: Frequency dependence,” MP-12, IEEE Trans. Biomed. Eng. 28:379-382 (1981)
Rijkhoff N J et al., “Acute animal studies on the use of anodal block to reduce urethral resistance in sacral root stimulation,” IEEE Transactions on Rehabilitation Engineering, 2(2):92 (1994)
Mushahwar V K et al., “Muscle recruitment through electrical stimulation of the lumbo-sacral spinal cord,” IEEE Trans Rehabil Eng, 8(1):22-9 (2000)
Deurloo K E et al., “Transverse tripolar stimulation of peripheral nerve: a modelling study of spatial selectivity,” Med Biol Eng Comput, 36(1):66-74 (1998)
Tarver W B et al., “Clinical experience with a helical bipolar stimulating lead,” Pace, Vol. 15, October, Part II (1992)
Manfredi M, “Differential block of conduction of larger fibers in peripheral nerve by direct current,” Arch. Ital. Biol., 108:52-71 (1970)
In physiological muscle contraction, nerve fibers are recruited in the order of increasing size, from smaller-diameter fibers to progressively larger-diameter fibers. In contrast, artificial electrical stimulation of nerves using standard techniques recruits fibers in a larger- to smaller-diameter order, because larger-diameter fibers have a lower excitation threshold. This unnatural recruitment order causes muscle fatigue and poor force gradation. Techniques have been explored to mimic the natural order of recruitment when performing artificial stimulation of nerves to stimulate muscles.
Fitzpatrick et al., in “A nerve cuff design for the selective activation and blocking of myelinated nerve fibers,” Ann. Conf. of the IEEE Eng. in Medicine and Biology Soc, 13(2), 906 (1991), which is incorporated herein by reference, describe a tripolar electrode used for muscle control. The electrode includes a central cathode flanked on its opposite sides by two anodes. The central cathode generates action potentials in the motor nerve fiber by cathodic stimulation. One of the anodes produces a complete anodal block in one direction so that the action potential produced by the cathode is unidirectional. The other anode produces a selective anodal block to permit passage of the action potential in the opposite direction through selected motor nerve fibers to produce the desired muscle stimulation or suppression.
The following articles, which are incorporated herein by reference, may be of interest:
Rijkhoff N J et al., “Orderly recruitment of motoneurons in an acute rabbit model,” Ann. Conf. of the IEEE Eng., Medicine and Biology Soc., 20(5):2564 (1998)
Rijkhoff N J et al., “Selective stimulation of small diameter nerve fibers in a mixed bundle,” Proceedings of the Annual Project Meeting Sensations/Neuros and Mid-Term Review Meeting on the TMR-Network Neuros, Apr. 21-23, 1999, pp. 20-21 (1999)
Baratta R et al., “Orderly stimulation of skeletal muscle motor units with tripolar nerve cuff electrode,” IEEE Transactions on Biomedical Engineering, 36(8):836-43 (1989)
Levy M N, Blattberg B., “Effect of vagal stimulation on the overflow of norepinephrine into the coronary sinus during sympathetic nerve stimulation in the dog,” Circ Res 1976 February; 38(2):81-4
Lavallee et al. “Muscarinic inhibition of endogenous myocardial catecholamine liberation in the dog,” Can J Physiol Pharmacol 1978 August; 56(4):642-9
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Barzilai A, Daily D, Zilkha-Falb R, Ziv I, Offen D, Melamed E, Sirv A, “The molecular mechanisms of dopamine toxicity,” Adv Neurol 2003; 91:73-82
The following articles, which are incorporated herein by reference, describe techniques using point electrodes to selectively excite peripheral nerve fibers:
Grill W M et al., “Inversion of the current-distance relationship by transient depolarization,” IEEE Trans Biomed Eng, 44(1):1-9 (1997)
Goodall E V et al., “Position-selective activation of peripheral nerve fibers with a cuff electrode,” IEEE Trans Biomed Eng, 43(8):851-6 (1996)
Veraart C et al., “Selective control of muscle activation with a multipolar nerve cuff electrode,” IEEE Trans Biomed Eng, 40(7):640-53 (1993)
As defined by Rattay, in the article, “Analysis of models for extracellular fiber stimulation,” IEEE Transactions on Biomedical Engineering, Vol. 36, no. 2, p. 676, 1989, which is incorporated herein by reference, the activation function (AF) is the second spatial derivative of the electric potential along an axon. In the region where the activation function is positive, the axon depolarizes, and in the region where the activation function is negative, the axon hyperpolarizes. If the activation function is sufficiently positive, then the depolarization will cause the axon to generate an action potential; similarly, if the activation function is sufficiently negative, then local blocking of action potentials transmission occurs. The activation function depends on the current applied, as well as the geometry of the electrodes and of the axon.
For a given electrode geometry, the equation governing the electrical potential is:∇(σ∇U)=4πj, 
where U is the potential, σ is the conductance tensor specifying the conductance of the various materials (electrode housing, axon, intracellular fluid, etc.), and j is a scalar function representing the current source density specifying the locations of current injection.